Stars
I think they are eyes,
blinking in deep somnolence
to midnight nocturne.
a sheet of argus
spanning skies from edge to edge,
soon swallowed by dawn.
flames to the cold moon;
celestial attendants
to their marble queen.
or, perhaps, seraphsemblazoned in indigo.
night’s vigilantes
casting mosaics
onto the placid faces
of silent, glass lakes.
Then, like a dream,
they leave no trace of their faint
faint existences.

The exact location of the scene varies by cast and medium (because, at the time of this writeup, there have been several different casts, recasts and at least one Hollywood movie) but the sentiment is always the same: Javert sings about his intention to catch Jean Valjean at all costs:

There, out in the darkness
a fugitive running
fallen from God
fallen from grace

Javert expresses his near obsession with catching this fugitive who, in his eyes, is a criminal because he broke the law and not because of the intentions and/or consequences of his actions (see:Deontology, Consequentialism). Valjean is an agent of chaos and that is the greatest crime in Javert's eyes. In order to make his point, he refers to the stars as an (incorrect, see below) example of how the universe is somehow fixed and follows strict, unchangeable rules:

You know your place in the sky
You hold your course and your aim
And each in your season
Returns and returns
And is always the same

Thus Javert sees himself as an agent of order, who swears to bring Valjean to (his own particular view of) justice.

Pretty much every major character in Les Misérables has their own solo. For the other ones, see:

Of course, in the 21st century we know that the stars are not "fixed" in the sky, but are constantly moving along with our own sun and solar system. However, these changes are imperceptible in a single lifetime as it takes millenia to detect even the smallest movements. At this moment I'm not sure of the astronomical knowledge of the early 19th century and thus I can't say if this was even common knowledge to the layman then. It's easier to describe Javert as someone who most likely would make this comparison even if he knew about this non-fixed universe (also because it would be a lot harder to write a song using perfectly fixed physical phenomena--if they even exist)